کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416633 | 1336835 | 2013 | 21 صفحه PDF | دانلود رایگان |
In this paper, we consider matrices with entries from a semiring S. We first discuss some generalized inverses of rectangular and square matrices. We establish necessary and sufficient conditions for the existence of the Moore-Penrose inverse of a regular matrix. For an mÃn matrix A, an nÃm matrix P and a square matrix Q of order m, we present necessary and sufficient conditions for the existence of the group inverse of QAP with the additional property that P(QAP)#Q is a {1,2} inverse of A. The matrix product used here is the usual matrix multiplication. The result provides a method for generating elements in the set of {1,2} inverses of an mÃn matrix A starting from an initial {1} inverse of A. We also establish a criterion for the existence of the group inverse of a regular square matrix. We then consider a semiring structure (MmÃn(S),+,â) made up of mÃn matrices with the addition defined entry-wise and the multiplication defined as in the case of the Hadamard product of complex matrices. In the semiring (MmÃn(S),+,â), we present criteria for the existence of the Drazin inverse and the Moore-Penrose inverse of an mÃn matrix. When S is commutative, we show that the Hadamard product preserves the Hermitian property, and provide a Schur-type product theorem for the product Aâ(CCâ) of a positive semidefinite nÃn matrix A and an nÃn matrix C.
Journal: Linear Algebra and its Applications - Volume 439, Issue 7, 1 October 2013, Pages 2085-2105